Sign-constrained robust least squares, subjective breakdown point and the effect of weights of observations on robustness

The findings of this paper are summarized as follows: (1) We propose a sign-constrained robust estimation method, which can tolerate 50% of data contamination and meanwhile achieve high, least-squares-comparable efficiency. Since the objective function is identical with least squares, the method may also be called sign-constrained robust least squares. An iterative version of the method has been implemented and shown to be capable of resisting against more than 50% of contamination. As a by-product, a robust estimate of scale parameter can also be obtained. Unlike the least median of squares method and repeated medians, which use a least possible number of data to derive the solution, the sign-constrained robust least squares method attempts to employ a maximum possible number of good data to derive the robust solution, and thus will not be affected by partial near multi-collinearity among part of the data or if some of the data are clustered together; (2) although M-estimates have been reported to have a breakdown point of 1/(t+1), we have shown that the weights of observations can readily deteriorate such results and bring the breakdown point of M-estimates of Huber’s type to zero. The same zero breakdown point of the L ₁-norm method is also derived, again due to the weights of observations; (3) by assuming a prior distribution for the signs of outliers, we have developed the concept of subjective breakdown point, which may be thought of as an extension of stochastic breakdown by Donoho and Huber but can be important in explaining real-life problems in Earth Sciences and image reconstruction; and finally, (4) We have shown that the least median of squares method can still break down with a single outlier, even if no highly concentrated good data nor highly concentrated outliers exist. An erratum to this article is available at .     

广域差分参考站两种伪距平滑算法的再评估

广域差分GPS系统（WADGPS）参考站上，需要利用载波相位平滑伪距算法来减小多路径效应的影响。伪距平滑算法有Hatch滤波和加权Hatch滤波两种。文中基于我国WADGPS参考站的实际数据，对这两种平滑算法进行重新评估。实际数据显示，如果不能获得可靠的伪距观测值的方差，在抑制伪距中噪声的影响方面，Hatch滤波明显优于加权Hatch滤波。     

中值滤波技术在遥感图像处理中的应用

利用中值滤波技术能够很好的抑制噪声和保护边缘信息这一特性,用不同的滤波窗口对遥感图像进行处理,并做出处理后图像的归一化差值图像。通过图形分析发现差值图像上的信息比原始图像细节信息更丰富,某些地质现象更清晰。     

福建省矿山环境现状及区划研究

根据福建省矿山环境现状、地质环境条件、矿产资源开发利用规划、矿山环境恢复治理难易程度等矿山地质环境问题评价因子,采用加权指数模型,通过对各因子的评判、叠加,圈出矿山地质环境质量指数等值线,将福建省矿山地质环境划分为严重区、较严重区、一般区等3个区域。     

Distribution of diatoms among intermittent ponds on the Atlantic Coastal Plain: development of a model to preduct drought periodicity from surface-sediment assemblages

Inferences of past climate from the fossil record in lakes rely on the accurate quantification of a relationship of fossilizing organisms to their environment. Whereas the relationship of diatoms to water chemistry parameters has been modeled in many systems, few studies adequately address the relationship of diatoms to physical properties, such as water depth or hydrology, that may be more directly tied to climate. We examined the composition of modern diatoms in surface sediments of 75 isolated ponds (mostly Carolina bays) of the Atlantic Coastal Plain to: (1) assess the influence of physical and chemical variables on the distribution of diatoms among ponds of the region, and (2) develop a model that predicts hydroperiod (a measure of pond permanence) from diatom assemblages. We constructed two hydroperiod calibration models: the first infers hydroperiod from the weighted-average optima and tolerances of taxa along the hydroperiod gradient, the second bases inferences on the hydroperiod estimates of compositionally similar samples. Both approaches incorporate a-priori and post-hoc tests of assumptions often inherent in the construction of transfer functions. Diatom assemblage composition had strong, approximately linear relationships to hydroperiod, water depth, and calcium concentration in non-metric multidimensional ordination space; effects of other variables, including pH, were non-linear or ambiguous. Overall, the assemblages reflected the dilute, acidic chemical characteristics of bays. The assemblages contained differing abundances of euterrestrial, benthic and planktonic taxa, depending on a pond's susceptibility to drying. A weighted-averaging regression model based on taxon-specific hydroperiod optima generated adequate, unbiased hydroperiod inferences from diatom species composition (r² = 0.81). This model may be used to infer past drought episodes from fossil diatom assemblages at appropriate sites on the Atlantic Coastal Plain.     

论不连序系列样本概率权重矩不偏计算公式

人们普遍认为要从理论上通过数学分析的方法来论证不连序系列样本概率权重矩的偏倚性是很困难的。本文根据次序统计量理论，分析推证了不连序系列样本概率权重矩的不偏计算公式，论证结果具有较重要的理论和实用意义。     

Diatom-based water chemistry reconstructions from northern Sweden: a comparison of reconstruction techniques

The diatom composition in surface sediments from 119 northern Swedish lakes was studied to examine the relationship with lake-water pH, alkalinity, and colour. Diatom-based predictive models, using weighted-averaging (WA) regression and calibration, partial least squares (PLS) regression and calibration, and weighted-averaging partial least squares (WA-PLS) regression and calibration, were developed for inferences of water chemistry conditions. The non-linear response between the diatom assemblages and pH and alkalinity was best modelled by weighted-averaging methods. The lowest prediction error for pH was obtained using weighted averaging, with or without tolerance downweighting. For alkalinity there was still some information in the residual structure after extracting the first weighted-averaging component, which resulted in a slight improvement of predictions when using a two component WA-PLS model. The best colour predictions were obtained using a two component PLS model. Principal component analysis (PCA) of the prediction errors, with some characteristics of the training set included as passive variables, was performed to compare the results for the different alkalinity predictive models. The results indicate that calibration techniques utilizing more than one component (PLS and WA-PLS) can improve the predictions for lakes with diatom taxa that have broad tolerances. Furthermore, we show that WA-PLS performs best compared with the other techniques for those lakes that have a high relative abundance of the most dominant taxa and a corresponding low sample heterogeneity.     

一种矢径最短的抛物线加权平均光滑插值法

本文提出了一种抛物线加权平均曲线光滑插值算法。它满足了一个特殊的要求，即曲线通过全部节点且到弦的垂直距离最短。同时，将张力系数引入该方法中，并给出了包含张力系数的光滑方程。     

选权迭代定位粗差时权函数参数之功能

本文研究了幂函数型权函数的参数与定位粗差能力的关系。提出了权函数基本变量的幂取值范围为-2.5～-4.0;计算权的基本变量对于第1,2次迭代用“放大余差”,以后则用余差;对余差进行统计判断的统计量采用“标准化余差”。